Fair allocation of conflicting items

We study fair allocation of indivisible items, where the items are furnished with a set of conflicts, and agents are not permitted to receive conflicting items. This kind of constraint captures, for example, participating in events that overlap in time, or taking on roles in the presence of conflicting interests. We demonstrate, both theoretically and experimentally, that fairness characterizations such as EF1, MMS and MNW still are applicable and useful under item conflicts. Among other existence, non-existence and computability results, we show that a $$1/\Delta $$ 1 / Δ -approximate MMS allocation for n agents may be found in polynomial time when $$n>\Delta >2$$ n > Δ > 2 , for any conflict graph with maximum degree $$\Delta$$ Δ , and that, if $$n > \Delta $$ n > Δ , a 1/3-approximate MMS allocation always exists.

Optimization of data allocation in hierarchical memory for blocked shortest paths algorithms

This paper is devoted to the reduction of data transfer between the main memory and direct mapped cache for blocked shortest paths algorithms (BSPA), which represent data by a D[M×M] matrix of blocks. For large graphs, the cache size S = δ×M2, δ < 1 is smaller than the matrix size. The cache assigns a group of main memory blocks to a single cache block. BSPA performs multiple recalculations of a block over one or two other blocks and may access up to three blocks simultaneously. If the blocks are assigned to the same cache block, conflicts occur among the blocks, which imply active transfer of data between memory levels. The distribution of blocks on groups and the block conflict count strongly depends on the allocation and ordering of the matrix blocks in main memory. To solve the problem of optimal block allocation, the paper introduces a block conflict weighted graph and recognizes two cases of block mapping: non-conflict and minimum-conflict. In first case, it formulates an equitable color-class-size constrained coloring problem on the conflict graph and solves it by developing deterministic and random algorithms. In second case, the paper formulates a problem of weighted defective color-count constrained coloring of the conflict graph and solves it by developing a random algorithm. Experimental results show that the equitable random algorithm provides an upper bound of the cache size that is very close to the lower bound estimated over the size of a complete subgraph, and show that a non-conflict matrix allocation is possible at δ = 0.5 for M = 4 and at δ = 0.1 for M = 20. For a low cache size, the weighted defective algorithm gives the number of remaining conflicts that is up to 8.8 times less than the original BSPA gives. The proposed model and algorithms are applicable to set-associative cache as well.

Drug repurposing based on a Quantum-Inspired method versus classical fingerprinting uncovers potential antivirals against SARS-CoV-2 including vitamin B12

The COVID-19 pandemic has accelerated the need to identify new therapeutics at pace, including through drug repurposing. We employed a Quadratic Unbounded Binary Optimization (QUBO) model, to search for compounds similar to Remdesivir (RDV), the only antiviral against SARS-CoV-2 currently approved for human use, using a quantum-inspired device. We modelled RDV and compounds present in the DrugBank database as graphs, established the optimal parameters in our algorithm and resolved the Maximum Weighted Independent Set problem within the conflict graph generated. We also employed a traditional Tanimoto fingerprint model. The two methods yielded different lists of compounds, with some overlap. While GS-6620 was the top compound predicted by both models, the QUBO model predicted BMS-986094 as second best. The Tanimoto model predicted different forms of cobalamin, also known as vitamin B12. We then determined the half maximal inhibitory concentration (IC50) values in cell culture models of SARS-CoV-2 infection and assessed cytotoxicity. Lastly, we demonstrated efficacy against several variants including SARS-CoV-2 Strain England 2 (England 02/2020/407073), B.1.1.7 (Alpha), B.1.351 (Beta) and B.1.617.2 (Delta). Our data reveal that BMS-986094 and different forms of vitamin B12 are effective at inhibiting replication of all these variants of SARS-CoV-2. While BMS-986094 can cause secondary effects in humans as established by phase II trials, these findings suggest that vitamin B12 deserves consideration as a SARS-CoV-2 antiviral, particularly given its extended use and lack of toxicity in humans, and its availability and affordability. Our screening method can be employed in future searches for novel pharmacologic inhibitors, thus providing an approach for accelerating drug deployment.

Delay minimization based uplink resource allocation for device-to-device communications considering mmWave propagation

This paper addresses the resource allocation problem in multi-sharing uplink for device-to-device (D2D) communication, one aspect of 5G communication networks. The main advantage and motivation in relation to the use of D2D communication is the significant improvement in the spectral efficiency of the system when exploiting the proximity of communication pairs and reusing idle resources of the network, mainly in the uplink mode, where there are more idle available resources. An approach is proposed for allocating resources to D2D and cellular user equipments (CUE) users in the uplink of a 5G based network which considers the estimation of delay bound value. The proposed algorithm considers minimization of total delay for users in the uplink and solves the problem by forming conflict graph and by finding the maximal weight independent set. For the user delay estimation, an approach is proposed that considers the multifractal traffic envelope process and service curve for the uplink. The performance of the algorithm is evaluated through computer simulations in comparison with those of other algorithms in the literature in terms of throughput, delay, fairness and computational complexity in a scenario with channel modeling that describes the propagation of millimeter waves at frequencies above 6 GHz. Simulation results show that the proposed allocation algorithm outperforms other algorithms in the literature, being highly efficient to 5G systems.

Orbital Conflict: Cutting Planes for Symmetric Integer Programs

Cutting planes have been an important factor in the impressive progress made by integer programming (IP) solvers in the past two decades. However, cutting planes have had little impact on improving performance for symmetric IPs. Rather, the main breakthroughs for solving symmetric IPs have been achieved by cleverly exploiting symmetry in the enumeration phase of branch and bound. In this work, we introduce a hierarchy of cutting planes that arise from a reinterpretation of symmetry-exploiting branching methods. There are too many inequalities in the hierarchy to be used efficiently in a direct manner. However, the lowest levels of this cutting-plane hierarchy can be implicitly exploited by enhancing the conflict graph of the integer programming instance and by generating inequalities such as clique cuts valid for the stable set relaxation of the instance. We provide computational evidence that the resulting symmetry-powered clique cuts can improve state-of-the-art symmetry-exploiting methods. The inequalities are then employed in a two-phase approach with high-throughput computations to solve heretofore unsolved symmetric integer programs arising from covering designs, establishing for the first time the covering radii of two binary-ternary codes.

Computational aspects of infeasibility analysis in mixed integer programming

The analysis of infeasible subproblems plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. There are two fundamentally different concepts to generate valid global constraints from infeasible subproblems: conflict graph analysis and dual proof analysis. While conflict graph analysis detects sets of contradicting variable bounds in an implication graph, dual proof analysis derives valid linear constraints from the proof of the dual LP’s unboundedness. The main contribution of this paper is twofold. Firstly, we present three enhancements of dual proof analysis: presolving via variable cancellation, strengthening by applying mixed integer rounding functions, and a filtering mechanism. Further, we provide a comprehensive computational study evaluating the impact of every presented component regarding dual proof analysis. Secondly, this paper presents the first combined approach that uses both conflict graph and dual proof analysis simultaneously within a single MIP solution process. All experiments are carried out on general MIP instances from the standard public test set Miplib 2017; the presented algorithms have been implemented within the non-commercial MIP solver and the commercial MIP solver .